The wavelength of spectral line obtained in the spectrum of ion, when the transition takes place between two levels whose sum is 4 and difference is 2, is [2026]

Question

The wavelength of spectral line obtained in the spectrum of ${Li}^{2 +}$ ion, when the transition takes place between two levels whose sum is 4 and difference is 2, is [2026]

Smart Achievers · Accepted Answer

(3)

$n_{1} \to lower energy level$

$n_{2} \to higher energy level$

$n_{1} + n_{2} = 4, n_{2} = 3$

$n_{2} - n_{1} = 2, n_{1} = 1$

$Rydberg's formula:$

$\frac{1}{λ} = R_{H} Z^{2} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}]$

$\frac{1}{λ} = R_{H} {(3)}^{2} [\frac{1}{1^{2}} - \frac{1}{3^{2}}]$

$\frac{1}{λ} = 8 R_{H}$

$λ = \frac{1}{8 R_{H}}$

$λ = \frac{1}{8 \times 1.1 \times 10^{5}}$

$λ = \frac{1000}{8.8} \times 10^{- 8} cm$

$λ = 113.63 \times 10^{- 8} cm$

$λ \approx 1.14 \times 10^{- 6} cm$

Solution

Q.
The wavelength of spectral line obtained in the spectrum of ${Li}^{2 +}$ ion, when the transition takes place between two levels whose sum is 4 and difference is 2, is [2026]

1 $2.28 \times 10^{- 7} cm$

2 $2.28 \times 10^{- 6} cm$

3 $1.14 \times 10^{- 6} cm$

4 $1.14 \times 10^{- 7} cm$

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Solution

Q. The wavelength of spectral line obtained in the spectrum of Li2+ ion, when the transition takes place between two levels whose sum is 4 and difference is 2, is [2026]

1 2.28×10-7 cm

2 2.28×10-6 cm

3 1.14×10-6 cm

4 1.14×10-7 cm